Fast update algorithm for the quantum Monte Carlo simulation of the Hubbard model

Abstract

This paper presents an efficient algorithm for computing the transition probability in auxiliary field quantum Monte Carlo simulations of strongly correlated electron systems using a Hubbard model. This algorithm is based on a low rank updating of the underlying linear algebra problem, and results in significant computational savings. The computational complexity of computing the transition probability and Green’s function update reduces to O(k2) during the kth step, where k is the number of accepted spin flips, and results in an algorithm that is faster than the competing delayed update algorithm. Moreover, this algorithm is orders of magnitude faster than traditional algorithms that use naive updating of the Green’s function matrix.